Green’s Dictionary of Slang

(US) a member of the trade union Industrial Workers of the World or IWW.

1914		‘Overalls and Snuff’ in Lingenfelter et al. Songs of the Amer. West (1968) 496: I knew he was a Wobbly by the button that he wore.
1921		P. & T. Casey Gay-cat 192: Sure, a Wobbly, an I.W.W., a carrier o’ the red card that will yit be the flag o’ industrial freedom fur the world!
1930		(con. 1910s) Dos Passos 42nd Parallel in USA (1966) 91: They lynched the pacifists and the pro-Germans and the wobblies and the reds and the bolsheviks.
1939		K. Tennant Foveaux 96: The cost of living had risen enormously and wages had not; but if you grumbled about it you were likely to be labelled a ‘wobblie’ or a pro-German.
1945		H.B. Darrach Jr. ‘Sticktown Nocturne’ in Baltimore Sun (MD) 12 Aug. A-1/5: [headline] Wobblies Yielded to Pressure.
1956		F.O. Beck Hobohemia 15: The majority of these migratory workers are members of the Industrial Workers of the World — ‘Wobblies.’.
1967		W. Manus Mott the Hoople 96: Some were pacifists, [...] some old-time wobblies.
1987		(con. 1967) Bunch & Cole Reckoning for Kings (1989) 51: Stories about working stiffs – like us. Commies. Wobblies.